Center of mass

A lattice is on the portion of the disk in the first quadrant. Find its center of mass if the density at any point is proportional to its distance with the axis.
My attempt : I first calculated the total mass of the lattice which gave me , where is the constant of proportionality.
Then I found out that the center of mass is located at .

I just want to know if this is the correct result because I find it quite strange.

A lattice is on the portion of the disk in the first quadrant. Find its center of mass if the density at any point is proportional to its distance with the axis.
My attempt : I first calculated the total mass of the lattice which gave me , where is the constant of proportionality.
Then I found out that the center of mass is located at .

I just want to know if this is the correct result because I find it quite strange.

Originally Posted by HallsofIvy

Two things I notice immediately are that the figure and density function are both symmetric in x and y. The x and y coordinates of the center of mass must be the same.